Error exponents for Orthogonal STBC in generalized-K fading MIMO channels

In this paper, we study the error exponent of generalized-K fading multiple-input multiple-output (MIMO) channels over Orthogonal Space-Time Block Codes (OSTBC). Error exponent sets ultimate bounds on the performance of communication systems employing codes of finite complexity and has been seen as one of the most significant information theoretic measures of reliability. In this paper, closed-form expressions of Gallager´s random coding and expurgated error exponents for generalized-K fading MIMO channels over OSTBC are derived, assuming that there is no channel-state information (CSI) at the transmitter and perfect CSI at the receiver. Based on which, we gain valuable insight into the fundamental tradeoff between the communication reliability and information rate of the channel. The necessary codeword length to achieve predefined error probability at a given rate below the capacity of channel is identified. Moreover, we derive closed-form expressions for the cutoff rate, critical rate and expurgation rate.